Question

The volume of a cylinder of height 8 cm is 1232 cm³. Find its curved surface area and the total surface area.

Answer 1

Height = 8 cm
Volume$={\mathrm{\pi r}}^2\mathrm{h}=1232{\mathrm{cm}}^3$
Now, radius$=r=\sqrt{\frac{1232}{\mathrm{\pi h}}}=\sqrt{\frac{1232\times 7}{22\times 8}}=\sqrt{49}=7cm$
Also, curved surface area $=2\mathrm{\pi rh}=2\times \frac{22}{7}\times 7\times 8=352{\mathrm{cm}}^2$
∴ Total surface area $=2\mathrm{\pi r}(\mathrm{h}+\mathrm{r})=\left(2\times \frac{22}{7}\times 7\times 8\right)+\left(2\times \frac{22}{7}\times {\left(7\right)}^2\right)=352+308=660{\mathrm{cm}}^2$